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Abstract
Iterative schemes to find steadystate solutions to the Boltzmann equation is efficient for highly rarefied gas flows, but can be very slow to converge in the nearcontinuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator $L$ into the form $L=(L+N\delta{h})N\delta{h}$, where $\delta$ is the gas rarefaction parameter, $h$ is the velocity distribution function, and $N$ is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusiontype equation that is asymptoticpreserving into the NavierStokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when $N\delta$ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the nearcontinuum gas flow regimes. Moreover, due to its asymptoticpreserving properties, the synthetic iterative scheme does not need high spatial resolution in the nearcontinuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a NeAr gas mixture is solved based on the linearized Boltzmann equation with the LennardJones intermolecular potential for the first time, and the difference between these results and those using the hardsphere potential is discussed.
Original language  English 

Pages (fromto)  431–451 
Number of pages  21 
Journal  Journal of Computational Physics 
Volume  338 
Early online date  7 Mar 2017 
DOIs  
Publication status  Published  1 Jun 2017 
Keywords
 linearized Boltzmann equation
 rarefied gas dynamics
 synthetic iterative scheme
 LennardJones potential
 gas mixture
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Dive into the research topics of 'A fast iterative scheme for the linearized Boltzmann equation'. Together they form a unique fingerprint.Projects
 2 Finished

PoreScale Study of Gas Flows in Ultratight Porous Media
Zhang, Y. & Scanlon, T.
EPSRC (Engineering and Physical Sciences Research Council)
1/09/15 → 30/09/19
Project: Research

UK Consortium on Mesoscale Engineering Sciences (UKCOMES)
Zhang, Y.
EPSRC (Engineering and Physical Sciences Research Council)
1/06/13 → 31/05/18
Project: Research